Decision Matrix
Compare options on weighted criteria: weight each criterion 1 to 10, score each option 1 to 10 and see the weighted scores and the highest, ties included. How it works
Use the Decision Matrix
About the Decision Matrix
A weighted decision matrix scores each option as sum(score x weight) / sum(weights). In the starting example, with Price weighted 5 and Quality 8, Option A (scores 7 and 6) gets 83 / 13 = 6.38 and Option B (4 and 9) gets 92 / 13 = 7.08, the highest weighted score. Options equal to two decimals are tied and all of them are shown.
The starting example and two changes to it
| Matrix | Weights (shares) | Option A | Option B | Highest weighted score |
|---|---|---|---|---|
| Starting example: A scores 7 and 6, B scores 4 and 9 | Price 5 (38.46%), Quality 8 (61.54%) | 6.38 (total 83) | 7.08 (total 92) | Option B |
| Price weight raised to 10 | Price 10 (55.56%), Quality 8 (44.44%) | 6.56 (total 118) | 6.22 (total 112) | Option A |
| Equal weights, A scores 8 and 6, B scores 6 and 8 | Price 5 (50%), Quality 5 (50%) | 7.00 (total 70) | 7.00 (total 70) | Tie: Option A and Option B |
Weighted score = sum(score x weight) / sum(weights); the total is sum(score x weight).
Frequently asked questions
- How do you calculate a weighted decision matrix?
- Multiply each score by its criterion's weight, add the products and divide by the sum of the weights. For three flats with Rent weighted 9, Commute 6 and Space 4 (19 in all), Flat A scoring 6, 9 and 5 gets 128 / 19 = 6.74, Flat B (8, 5, 7) gets 130 / 19 = 6.84 and Flat C (7, 7, 6) gets 129 / 19 = 6.79, so Flat B has the highest weighted score by a small margin.
- What do the weight percentages mean?
- Each weight divided by the sum of the weights. Price 5 and Quality 8 add to 13, so their shares are 38.46% and 61.54%; Rent 9, Commute 6 and Space 4 are 47.37%, 31.58% and 21.05%. Only the proportions count, which is why the weighted score stays on the 1 to 10 scale of the scores.
- What happens if two options tie in a decision matrix?
- Options whose weighted scores are equal to two decimals are all shown as tied. With Price and Quality both at weight 5, Option A scoring 8 and 6 and Option B scoring 6 and 8 both get 70 / 10 = 7.00, and the page shows a tie for the highest weighted score: Option A and Option B (7.00 each).
- How do I know if the result depends on the weights?
- Read the Does the weight change the winner? panel. It moves each criterion's weight through 1 to 10, keeps the other weights as set, and lists who leads at each weight. In the starting example Option B leads at Price weights 1 to 7, Option A and Option B tie at 8, and Option A leads at 9 and 10: at 10, Option A scores 118 / 18 = 6.56 and Option B 112 / 18 = 6.22. When a small change of weight swaps the leader, the options are close on what you care about.
- Should a low price get a high score?
- Yes. The matrix adds scores, so a higher score has to mean better on every criterion: give the cheapest option the highest Price score, and the slowest commute the lowest Commute score.
- How should I choose the weights?
- Only the ratios between weights count, so pick a method and keep to it. Ranking: put the criteria in order, give the top one 10 and step down from there. Pairwise: take two criteria at a time and say how many times more one matters; if Quality matters about 1.6 times as much as Price, weights 5 and 8 say that, which are the 38.46% and 61.54% shares of the starting example. Budget: split a fixed number of points, such as 13 points as 5 to Price and 8 to Quality. Then check the Does the weight change the winner? panel to see whether the choice of method matters.
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